The Final and grades
Solutions in brief
Problem 1, “hang time’ (time in the air) of 4 seconds, initial angle of 50°, how far?
This is a projectile problem, one of the possible 4 or so I promised. If you found it in your notes, you would see that I did this problem, at least for 45 ° and I certainly indicated the changes needed for a different angle.
The things one has to remember about a projectile problem: 1) horizontal speed is constant, so distance is that speed times how long in the air 2) can find time to top of motion, since v_y = 0 there (read as v sub y) AND that which changes the y velocity is gravity – 9.8 (or 10) m/s^2. So velocity goes to 0 in 2 sec, so initial v_y = 2s X 9.8 m/s^2 = 19.6 m/s.
That’s equal to v_y= v_initial X sin (50 °), and the x component is v_x= v_initial X cos(50 °) (= v_y /tan(50 °), since tan (theta) = sin (theta)/cos (theta).
Time of flight X v_x = 4 sec X 19.6 m/s X1/tan (50 °)= 65.8 m
Problem 2: Weight from end of bar – this is like a “crane-boom” used in constructing high-rise buildings.
(Imagine the \’s make a solid diagonal line)
Three forces act on end of beam, the weight (=mg) down, the T of the cable at an undetermined angle, and the beam pushing outward, also undetermined. But they must vectorially add to zero. So the vertical component of the tension is just the mg of the weight (and the horizontal component of the tension is equal and opposite to the push of the beam, and therefore the force of the wall on the beam). The weight = 9.8 X 50 N = 490N
The length of the cable is 5 m and of the beam is 3 m, so the angle is cos^(-1) theta = 3/5
And Tension X sin theta = mg, T = 613.1 N (and the force on the end of the beam = 367.9 N
Problem 3 – Again the notes had the problem basically, though the seal sliding down the incline included the speed part.
I won’t try to draw it, but what we had was ma = mg(sin (theta) – mu X cos (theta)),
v^2 (- v_i^2) = 2 a d, d being the distance.
Plugging in, you find v = 2.45 m/s
Good luck to all of you. If you didn’t pass the math prep part, you really need to work on your math before you try for the physics – almost everyone needs more work on solving simple equations, including how to handle fractions and inverses ……….like 1/x= 1/a+1/b !